Question

A group of 65 new substance abuse counselors were tested for their understanding of a new confidentiality procedure. The highest test score was a 92; the mean was 88 and the range was 6. The next day, a counselor who was absent took the test and scored a 100. Indicate whether adding the late counselor’s score to the rest of the scores will increase, decrease or likely not change the following descriptive measures.

Median

Variance

Range

Standard Deviation

Answer 1

Answer)

Median is given by the middlemost number of arranged data

By arranged i mean arranged in ascending order

So, if a new value of 100 would be added which is higher than the previous highest value

So, median would shift one steo forward to the next value, which will obviously be higher than previous as the data is arranged in ascending order

So, median will increase.

Variance is = spread of data that is distance of data points from mean

Given mean is = 88 for 64 as one is absent

Sum of scores = 88*64

Now a new score is added which is 100

So new mean = (88*64+100)/65 = 88.18

Which is close to 88 only

And we got a value which is very far from 88.18

So. Variance will also increase.

Range is given by highest value - lowest value

Previously highest value was = 92

Range was 6

So, lowest value is 92-6 = 86

Now a new highest score is added, which is 100

So, new range is = 100-86 = 14

So, range will also increase

Standard deviation

Standard deviation is square root of variance

So, s.d will also increase